Exercise 127 Page 138

If two lines are parallel, then pairs of corresponding angles are equal. The converse of a conditional statement, q→ p, exchanges the hypothesis and conclusion of the conditional statement. If a pair of corresponding angles formed by two lines and a transversal are equal, then the two lines are parallel. By the Converse to the Corresponding Angles Theorem we know that the converse is true.

In $△ ABC$, if the sum of $m∠ A$, and $m∠ B$ is $110^(∘)$, then $m∠ C=70^(∘)$. Again, to get the converse of the conditional statement, q→ p, we exchange the hypothesis and conclusion. In $△ ABC,$ if angle C is $70^(∘)$, then the sum of angles A and B is $110^(∘)$. By the Triangle Angle Sum Theorem, we know that the converse is true.

If alternate interior angles formed by two lines cut by a transversal are not congruent, then the two lines are not parallel. Again, to get the converse of the conditional statement, q→ p, we exchange the hypothesis and conclusion. If two lines cut by a transversal that form alternate interior angles are not parallel, then those angles are not congruent. By the Alternate Interior Angles Theorem, we know that the converse is true.

If Johan throws coins in the fountain, then he loses his money. Again, to get the converse of the conditional statement, q→ p, we exchange the hypothesis and conclusion. If Johan loses money, then he throws coins in the fountain. This is false, as Johan could lose his money in other ways.